What are the key aspects of Vipassana that are not present in Samatha?

He asked "key aspects", don't answer him too much.

What are the key aspects of Vipassana that are not present in Samatha?

Comprehending 3 characteristics of whole clinging-aggregates.

What is the main difference in the method from a meditator's perspective?

Comprehending 3 characteristics of whole clinging-aggregates.

Labeling emotions and feelings are part of samatha or vipassana?

It is suttamayañāṇa. So, when you labeling emotions and feelings for samatha, it is samatha, such as in visuddhimagga kammaṭṭhānaggahananiddesa. But when you labeling emotions and feelings for vipassanā, it is vipassanā, such as in visuddhimagga khandhaniddesa.

Does Vipassana allows emotions to rise more freely to check it for what it is while Samatha tries to avoid paying attention to it by returning to the breath process?

No any meditation allows unwholesome arise. Because buddha taught samatha to the practitioner to clear unwholesome of the practitioner, before he wil meditate vipassanā:

You should develop concentration, bhikkhus. Concentrated, bhikkhus, a bhikkhu understands as it actually is.